Complete the exercises below. Given the colors observed for VO₄³⁻ (orthovanadate ion), CrO₄²⁻ (chromate ion), and MnO₄⁻ (permanganate ion) (see Exercise 23.84), what can you say about how the energy separation between the ligand orbitals and the empty d orbitals changes as a function of the oxidation state of the transition metal at the center of the tetrahedral anion?

Ligand Field Theory explains how the presence of ligands around a transition metal ion affects the energy levels of its d orbitals. In tetrahedral complexes, the d orbitals split into two sets with different energy levels due to the electrostatic interactions between the ligands and the metal ion. Understanding this splitting is crucial for analyzing the colors observed in the complexes, as the energy difference corresponds to the wavelengths of light absorbed.

The oxidation state of a transition metal influences the energy of its d orbitals. As the oxidation state increases, the effective nuclear charge experienced by the d electrons also increases, leading to a greater energy separation between the ligand orbitals and the d orbitals. This change can affect the color of the complex, as it alters the wavelengths of light absorbed and emitted.

The color observed in transition metal complexes is a result of the specific wavelengths of light absorbed by the electrons transitioning between different energy levels. The absorption spectra of these complexes can provide insights into the energy separation between the ligand orbitals and the d orbitals. By analyzing the colors of VO₄³⁻, CrO₄²⁻, and MnO₄⁻, one can infer how the oxidation state affects these energy separations and, consequently, the observed colors.